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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On finite simply reducible groups


Authors: L. S. Kazarin and V. V. Yanishevskiĭ
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 19 (2007), nomer 6.
Journal: St. Petersburg Math. J. 19 (2008), 931-951
MSC (2000): Primary 53A04; Secondary 52A40., 52A10
Published electronically: August 21, 2008
MathSciNet review: 2411640
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Abstract | References | Similar Articles | Additional Information

Abstract: A finite group $ G$ is said to be simply reducible ($ SR$-group) if it has the following two properties: 1) each element of $ G$ is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of $ G$ with multiplicities not exceeding 1. It is proved that a finite $ SR$-group is solvable if it has no composition factors isomorphic to the alternating groups $ A_5$ or $ A_6$.


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Additional Information

L. S. Kazarin
Affiliation: Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
Email: kazarin@uniyar.ac.ru

V. V. Yanishevskiĭ
Affiliation: Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
Email: yvitaliy@rambler.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-08-01028-5
PII: S 1061-0022(08)01028-5
Keywords: Group, subgroup, irreducible representation, character, tensor product, real element
Received by editor(s): February 14, 2007
Published electronically: August 21, 2008
Additional Notes: The first author was supported by RFBR (grant no. 05-01-01018)
Dedicated: Dedicated to the centenary of D. K. Faddeev’s birth
Article copyright: © Copyright 2008 American Mathematical Society